ASperGe: SM_mix.fr

File SM_mix.fr, 23.6 KB (added by Karen De Causmaecker, 13 years ago)

Standard Model model-file including the mixings

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
5(****** Adapted by A. Alloul for mass diagonalization ******)
6(****** ******)
7(****** Choose whether Feynman gauge is desired. ******)
8(****** If set to False, unitary gauge is assumed. ****)
9(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
10(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
11(***************************************************************************************************************)
12
13(* ************************** *)
14(* ***** Information ***** *)
15(* ************************** *)
16M$ModelName = "SM_mix";
17
18M$Information = {
19 Authors -> {"N. Christensen", "C. Duhr", "B. Fuks", "A. Alloul"},
20 Version -> "1.0.0",
21 Date -> "13. 12. 2012",
22 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)","IPHC Strasbourg / University of Strasbourg"},
23 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "benjamin.fuks@cnrs.in2p3.fr", "adam.alloul@iphc.cnrs.fr"},
24 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
25};
26
27FeynmanGauge = True;
28
29(* ************************** *)
30(* ***** Change log ***** *)
31(* ************************** *)
32
33(* v1.4.4: changed some definitions for mass diagonalization. *)
34(* v1.4.3: Adding mixing relations for automated mass diagonalization. *)
35(* v1.4.2: Set FeynmanGauge=True as default again. *)
36(* v1.4: Added SU(2) representation. *)
37(* -> Modification in the field declarations (doublets are added) *)
38(* -> Modification in the Lagrangian (much simpler). *)
39(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
40(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
41(* Updated parameters to PDG 2010. *)
42(* v1.2: Set FeynmanGauge=True as default. *)
43(* Set Gluonic ghosts to be included in both gauges. *)
44(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
45(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
46(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
47
48(* ************************** *)
49(* ***** vevs & mixings ***** *)
50(* ************************** *)
51M$vevs = { {Phi[2],vev} };
52
53M$MixingsDescription = {
54 Mix["1u"] == {MassBasis -> {A, Z}, GaugeBasis -> {B, Wi[3]}, MixingMatrix -> UG, BlockName -> WEAKMIX},
55
56 Mix["2"] == {MassBasis -> {W, Wbar}, GaugeBasis -> {Wi[1], Wi[2]}, Value -> {{1/Sqrt[2], -I/Sqrt[2]}, {1/Sqrt[2], I/Sqrt[2]}}},
57
58 Mix["3a"] == {MassBasis -> {GP}, GaugeBasis -> {Phi[1]},Value -> {{-I}}},
59
60 Mix["3b"] == {MassBasis -> {{H}, {G0}}, GaugeBasis -> {Phi[2]},Value -> {{{1}}, {{1}}}},
61
62 Mix["4a"] == {MassBasis -> {dq[1, _], dq[2, _], dq[3, _]}, GaugeBasis -> {{QL[2, 1, _], QL[2, 2, _], QL[2, 3, _]}, {dR[1, _], dR[2, _],
63 dR[3, _]}}, MixingMatrix -> {CKM, _}, Value-> {_, {{1,0,0}, {0,1,0}, {0,0,1}} },Inverse -> {True, _}},
64
65 Mix["4b"] == {MassBasis -> {uq[1, _], uq[2, _], uq[3, _]}, GaugeBasis -> {{QL[1, 1, _], QL[1, 2, _], QL[1, 3, _]}, {uR[1, _], uR[2, _],
66 uR[3, _]}}, Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}},
67
68 Mix["5a"] == {MassBasis -> {l[1], l[2], l[3]}, GaugeBasis -> {{LL[2, 1], LL[2, 2], LL[2, 3]}, {lR[1], lR[2], lR[3]}},
69 Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}},
70
71 Mix["5b"] == {MassBasis -> {vl[1], vl[2], vl[3]}, GaugeBasis -> {LL[1, 1], LL[1, 2], LL[1, 3]},
72 Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}}}};
73
74
75(* ************************** *)
76(* ***** Gauge groups ***** *)
77(* ************************** *)
78M$GaugeGroups = {
79 U1Y == {
80 Abelian -> True,
81 CouplingConstant -> g1,
82 GaugeBoson -> B,
83 Charge -> Y
84 },
85 SU2L == {
86 Abelian -> False,
87 CouplingConstant -> gw,
88 GaugeBoson -> Wi,
89 StructureConstant -> Eps,
90 Representations -> {Ta,SU2D},
91 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
92 },
93 SU3C == {
94 Abelian -> False,
95 CouplingConstant -> gs,
96 GaugeBoson -> G,
97 StructureConstant -> f,
98 Representations -> {T,Colour},
99 DTerm -> dSUN
100 }
101};
102
103
104(* ************************** *)
105(* ***** Indices ***** *)
106(* ************************** *)
107
108IndexRange[Index[SU2W ]] = Unfold[Range[3]];
109IndexRange[Index[SU2D ]] = Unfold[Range[2]];
110IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
111IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
112IndexRange[Index[Generation]] = Range[3];
113
114IndexStyle[SU2W, j];
115IndexStyle[SU2D, k];
116IndexStyle[Gluon, a];
117IndexStyle[Colour, m];
118IndexStyle[Generation, f];
119
120
121(* ************************** *)
122(* *** Interaction orders *** *)
123(* *** (as used by mg5) *** *)
124(* ************************** *)
125
126M$InteractionOrderHierarchy = {
127 {QCD, 1},
128 {QED, 2}
129};
130
131
132(* ************************** *)
133(* **** Particle classes **** *)
134(* ************************** *)
135M$ClassesDescription = {
136
137(* Gauge bosons: physical vector fields *)
138 V[1] == {
139 ClassName -> A,
140 SelfConjugate -> True,
141 Mass -> 0,
142 Width -> 0,
143 ParticleName -> "a",
144 PDG -> 22,
145 PropagatorLabel -> "a",
146 PropagatorType -> W,
147 PropagatorArrow -> None,
148 FullName -> "Photon"
149 },
150 V[2] == {
151 ClassName -> Z,
152 SelfConjugate -> True,
153 Mass -> MZ,
154 Width -> {WZ, 2.4952},
155 ParticleName -> "Z",
156 PDG -> 23,
157 PropagatorLabel -> "Z",
158 PropagatorType -> Sine,
159 PropagatorArrow -> None,
160 FullName -> "Z"
161 },
162 V[3] == {
163 ClassName -> W,
164 SelfConjugate -> False,
165 Mass -> {MW,80.36},
166 Width -> {WW, 2.085},
167 ParticleName -> "W+",
168 AntiParticleName -> "W-",
169 QuantumNumbers -> {Q -> 1},
170 PDG -> 24,
171 PropagatorLabel -> "W",
172 PropagatorType -> Sine,
173 PropagatorArrow -> Forward,
174 FullName -> "W"
175 },
176 V[4] == {
177 ClassName -> G,
178 SelfConjugate -> True,
179 Indices -> {Index[Gluon]},
180 Mass -> 0,
181 Width -> 0,
182 ParticleName -> "g",
183 PDG -> 21,
184 PropagatorLabel -> "G",
185 PropagatorType -> C,
186 PropagatorArrow -> None,
187 FullName -> "G"
188 },
189
190(* Ghosts: related to physical gauge bosons *)
191 U[1] == {
192 ClassName -> ghA,
193 SelfConjugate -> False,
194 Ghost -> A,
195 QuantumNumbers -> {GhostNumber -> 1},
196 Mass -> 0,
197 PropagatorLabel -> "uA",
198 PropagatorType -> GhostDash,
199 PropagatorArrow -> Forward
200 },
201 U[2] == {
202 ClassName -> ghZ,
203 SelfConjugate -> False,
204 Ghost -> Z,
205 QuantumNumbers -> {GhostNumber -> 1},
206 Mass -> MZ,
207 PropagatorLabel -> "uZ",
208 PropagatorType -> GhostDash,
209 PropagatorArrow -> Forward
210 },
211 U[31] == {
212 ClassName -> ghWp,
213 SelfConjugate -> False,
214 Ghost -> W,
215 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
216 Mass -> {MW,80.36},
217 PropagatorLabel -> "uWp",
218 PropagatorType -> GhostDash,
219 PropagatorArrow -> Forward
220 },
221 U[32] == {
222 ClassName -> ghWm,
223 SelfConjugate -> False,
224 Ghost -> Wbar,
225 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
226 Mass -> {MW,80.36},
227 PropagatorLabel -> "uWm",
228 PropagatorType -> GhostDash,
229 PropagatorArrow -> Forward
230 },
231 U[4] == {
232 ClassName -> ghG,
233 SelfConjugate -> False,
234 Indices -> {Index[Gluon]},
235 Ghost -> G,
236 QuantumNumbers ->{GhostNumber -> 1},
237 Mass -> 0,
238 PropagatorLabel -> "uG",
239 PropagatorType -> GhostDash,
240 PropagatorArrow -> Forward
241 },
242
243(* Gauge bosons: unphysical vector fields *)
244 V[11] == {
245 ClassName -> B,
246 Unphysical -> True,
247 SelfConjugate -> True
248 },
249 V[12] == {
250 ClassName -> Wi,
251 Unphysical -> True,
252 SelfConjugate -> True,
253 Indices -> {Index[SU2W]},
254 FlavorIndex -> SU2W
255 },
256
257(* Ghosts: related to unphysical gauge bosons *)
258 U[11] == {
259 ClassName -> ghB,
260 Unphysical -> True,
261 SelfConjugate -> False,
262 Ghost -> B,
263 Definitions -> { ghB -> -(ee/gw) ghZ + (ee/g1) ghA}
264 },
265 U[12] == {
266 ClassName -> ghWi,
267 Unphysical -> True,
268 SelfConjugate -> False,
269 Ghost -> Wi,
270 Indices -> {Index[SU2W]},
271 FlavorIndex -> SU2W,
272 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> (ee/g1) ghZ+(ee/gw) ghA}
273 } ,
274
275(* Fermions: physical fields *)
276 F[1] == {
277 ClassName -> vl,
278 ClassMembers -> {ve,vm,vt},
279 Indices -> {Index[Generation]},
280 FlavorIndex -> Generation,
281 SelfConjugate -> False,
282 Mass -> 0,
283 Width -> 0,
284 QuantumNumbers -> {LeptonNumber -> 1},
285 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
286 PropagatorType -> S,
287 PropagatorArrow -> Forward,
288 PDG -> {12,14,16},
289 ParticleName -> {"ve","vm","vt"},
290 AntiParticleName -> {"ve~","vm~","vt~"},
291 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
292 },
293 F[2] == {
294 ClassName -> l,
295 ClassMembers -> {e, mu, ta},
296 Indices -> {Index[Generation]},
297 FlavorIndex -> Generation,
298 SelfConjugate -> False,
299 Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
300 Width -> 0,
301 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
302 PropagatorLabel -> {"l", "e", "mu", "ta"},
303 PropagatorType -> Straight,
304 PropagatorArrow -> Forward,
305 PDG -> {11, 13, 15},
306 ParticleName -> {"e-", "mu-", "ta-"},
307 AntiParticleName -> {"e+", "mu+", "ta+"},
308 FullName -> {"Electron", "Muon", "Tau"}
309 },
310 F[3] == {
311 ClassName -> uq,
312 ClassMembers -> {u, c, t},
313 Indices -> {Index[Generation], Index[Colour]},
314 FlavorIndex -> Generation,
315 SelfConjugate -> False,
316 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
317 Width -> {0, 0, {WT,1.50833649}},
318 QuantumNumbers -> {Q -> 2/3},
319 PropagatorLabel -> {"uq", "u", "c", "t"},
320 PropagatorType -> Straight,
321 PropagatorArrow -> Forward,
322 PDG -> {2, 4, 6},
323 ParticleName -> {"u", "c", "t" },
324 AntiParticleName -> {"u~", "c~", "t~"},
325 FullName -> {"u-quark", "c-quark", "t-quark"}
326 },
327 F[4] == {
328 ClassName -> dq,
329 ClassMembers -> {d, s, b},
330 Indices -> {Index[Generation], Index[Colour]},
331 FlavorIndex -> Generation,
332 SelfConjugate -> False,
333 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
334 Width -> 0,
335 QuantumNumbers -> {Q -> -1/3},
336 PropagatorLabel -> {"dq", "d", "s", "b"},
337 PropagatorType -> Straight,
338 PropagatorArrow -> Forward,
339 PDG -> {1,3,5},
340 ParticleName -> {"d", "s", "b" },
341 AntiParticleName -> {"d~", "s~", "b~"},
342 FullName -> {"d-quark", "s-quark", "b-quark"}
343 },
344
345(* Fermions: unphysical fields *)
346 F[11] == {
347 ClassName -> LL,
348 Unphysical -> True,
349 Indices -> {Index[SU2D], Index[Generation]},
350 FlavorIndex -> SU2D,
351 SelfConjugate -> False,
352 QuantumNumbers -> {Y -> -1/2}
353 },
354 F[12] == {
355 ClassName -> lR,
356 Unphysical -> True,
357 Indices -> {Index[Generation]},
358 FlavorIndex -> Generation,
359 SelfConjugate -> False,
360 QuantumNumbers -> {Y -> -1}
361 },
362 F[13] == {
363 ClassName -> QL,
364 Unphysical -> True,
365 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
366 FlavorIndex -> SU2D,
367 SelfConjugate -> False,
368 QuantumNumbers -> {Y -> 1/6}
369 },
370 F[14] == {
371 ClassName -> uR,
372 Unphysical -> True,
373 Indices -> {Index[Generation], Index[Colour]},
374 FlavorIndex -> Generation,
375 SelfConjugate -> False,
376 QuantumNumbers -> {Y -> 2/3}
377 },
378 F[15] == {
379 ClassName -> dR,
380 Unphysical -> True,
381 Indices -> {Index[Generation], Index[Colour]},
382 FlavorIndex -> Generation,
383 SelfConjugate -> False,
384 QuantumNumbers -> {Y -> -1/3}
385 },
386
387(* Higgs: physical scalars *)
388 S[1] == {
389 ClassName -> H,
390 SelfConjugate -> True,
391 Mass -> {MH,120},
392 Width -> {WH,0.00575308848},
393 PropagatorLabel -> "H",
394 PropagatorType -> D,
395 PropagatorArrow -> None,
396 PDG -> 25,
397 ParticleName -> "H",
398 FullName -> "H"
399 },
400
401 S[2] == {
402 ClassName -> G0,
403 SelfConjugate -> True,
404 Goldstone -> Z,
405 Mass -> MZ,
406 Width -> WGo,
407 PropagatorLabel -> "Go",
408 PropagatorType -> D,
409 PropagatorArrow -> None,
410 PDG -> 250,
411 ParticleName -> "G0",
412 FullName -> "G0"
413 },
414
415 S[3] == {
416 ClassName -> GP,
417 SelfConjugate -> False,
418 Goldstone -> W,
419 Mass -> {MW,80.36},
420 QuantumNumbers -> {Q -> 1},
421 Width -> WGP,
422 PropagatorLabel -> "GP",
423 PropagatorType -> D,
424 PropagatorArrow -> None,
425 PDG -> 251,
426 ParticleName -> "G+",
427 AntiParticleName -> "G-",
428 FullName -> "GP"
429 },
430
431(* Higgs: unphysical scalars *)
432 S[11] == {
433 ClassName -> Phi,
434 Unphysical -> True,
435 Indices -> {Index[SU2D]},
436 FlavorIndex -> SU2D,
437 SelfConjugate -> False,
438 QuantumNumbers -> {Y -> 1/2}
439 }
440};
441
442
443(* ************************** *)
444(* ***** Gauge ***** *)
445(* ***** Parameters ***** *)
446(* ***** (FeynArts) ***** *)
447(* ************************** *)
448
449GaugeXi[ V[1] ] = GaugeXi[A];
450GaugeXi[ V[2] ] = GaugeXi[Z];
451GaugeXi[ V[3] ] = GaugeXi[W];
452GaugeXi[ V[4] ] = GaugeXi[G];
453GaugeXi[ S[1] ] = 1;
454GaugeXi[ S[2] ] = GaugeXi[Z];
455GaugeXi[ S[3] ] = GaugeXi[W];
456GaugeXi[ U[1] ] = GaugeXi[A];
457GaugeXi[ U[2] ] = GaugeXi[Z];
458GaugeXi[ U[31] ] = GaugeXi[W];
459GaugeXi[ U[32] ] = GaugeXi[W];
460GaugeXi[ U[4] ] = GaugeXi[G];
461
462
463(* ************************** *)
464(* ***** Parameters ***** *)
465(* ************************** *)
466M$Parameters = {
467
468 (* External parameters *)
469 aEWM1 == {
470 ParameterType -> External,
471 BlockName -> SMINPUTS,
472 OrderBlock -> 1,
473 Value -> 127.9,
474 InteractionOrder -> {QED,-2},
475 Description -> "Inverse of the EW coupling constant at the Z pole"
476 },
477 Gf == {
478 ParameterType -> External,
479 BlockName -> SMINPUTS,
480 OrderBlock -> 2,
481 Value -> 1.16637*^-5,
482 InteractionOrder -> {QED,2},
483 TeX -> Subscript[G,f],
484 Description -> "Fermi constant"
485 },
486 aS == {
487 ParameterType -> External,
488 BlockName -> SMINPUTS,
489 OrderBlock -> 3,
490 Value -> 0.1184,
491 InteractionOrder -> {QCD,2},
492 TeX -> Subscript[\[Alpha],s],
493 Description -> "Strong coupling constant at the Z pole"
494 },
495 ymdo == {
496 ParameterType -> External,
497 BlockName -> YUKAWA,
498 OrderBlock -> 1,
499 Value -> 5.04*^-3,
500 Description -> "Down Yukawa mass"
501 },
502 ymup == {
503 ParameterType -> External,
504 BlockName -> YUKAWA,
505 OrderBlock -> 2,
506 Value -> 2.55*^-3,
507 Description -> "Up Yukawa mass"
508 },
509 yms == {
510 ParameterType -> External,
511 BlockName -> YUKAWA,
512 OrderBlock -> 3,
513 Value -> 0.101,
514 Description -> "Strange Yukawa mass"
515 },
516 ymc == {
517 ParameterType -> External,
518 BlockName -> YUKAWA,
519 OrderBlock -> 4,
520 Value -> 1.27,
521 Description -> "Charm Yukawa mass"
522 },
523 ymb == {
524 ParameterType -> External,
525 BlockName -> YUKAWA,
526 OrderBlock -> 5,
527 Value -> 4.7,
528 Description -> "Bottom Yukawa mass"
529 },
530 ymt == {
531 ParameterType -> External,
532 BlockName -> YUKAWA,
533 OrderBlock -> 6,
534 Value -> 172,
535 Description -> "Top Yukawa mass"
536 },
537 yme == {
538 ParameterType -> External,
539 BlockName -> YUKAWA,
540 OrderBlock -> 11,
541 Value -> 5.11*^-4,
542 Description -> "Electron Yukawa mass"
543 },
544 ymm == {
545 ParameterType -> External,
546 BlockName -> YUKAWA,
547 OrderBlock -> 13,
548 Value -> 0.10566,
549 Description -> "Muon Yukawa mass"
550 },
551 ymtau == {
552 ParameterType -> External,
553 BlockName -> YUKAWA,
554 OrderBlock -> 15,
555 Value -> 1.777,
556 Description -> "Tau Yukawa mass"
557 },
558 cabi == {
559 ParameterType -> External,
560 BlockName -> CKMBLOCK,
561 OrderBlock -> 1,
562 Value -> 0.227736,
563 TeX -> Subscript[\[Theta], c],
564 Description -> "Cabibbo angle"
565 },
566 (*Adam Modifs: 09/17/12*)
567 gw == {
568 ParameterType -> External,
569 BlockName -> Gauge,
570 OrderBlock -> 2,
571 Value -> 0.663922,
572 InteractionOrder -> {QED,1},
573 TeX -> Subscript[g,w],
574 Description -> "Weak coupling constant at the Z pole"
575 },
576 g1 == {
577 ParameterType -> External,
578 BlockName -> Gauge,
579 OrderBlock -> 1,
580 Value -> 0.355574,
581 InteractionOrder -> {QED,1},
582 TeX -> Subscript[g,1],
583 Description -> "U(1)Y coupling constant at the Z pole"
584 },
585 vev == {
586 ParameterType -> External,
587 BlockName -> HMIX,
588 OrderBlock -> 3,
589 Value -> 246,
590 InteractionOrder -> {QED,-1},
591 Description -> "Higgs vacuum expectation value"
592 },
593 (* Internal Parameters *)
594 aEW == {
595 ParameterType -> Internal,
596 Value -> 1/aEWM1,
597 InteractionOrder -> {QED,2},
598 TeX -> Subscript[\[Alpha], EW],
599 Description -> "Electroweak coupling contant"
600 },
601
602 ee == {
603 ParameterType -> Internal,
604 Value -> Sqrt[4 Pi aEW],
605 InteractionOrder -> {QED,1},
606 TeX -> e,
607 Description -> "Electric coupling constant"
608 },
609 gs == {
610 ParameterType -> Internal,
611 Value -> Sqrt[4*Pi*aS],
612 InteractionOrder -> {QCD,1},
613 TeX -> Subscript[g,s],
614 ParameterName -> G,
615 Description -> "Strong coupling constant at the Z pole"
616 },
617
618 yl == {
619 ParameterType -> Internal,
620 Indices -> {Index[Generation], Index[Generation]},
621 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
622 Value -> {yl[1,1] -> Sqrt[2] yme/vev, yl[2,2] -> Sqrt[2] ymm/vev, yl[3,3] -> Sqrt[2] ymtau/vev},
623 InteractionOrder -> {QED, 1},
624 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
625 TeX -> Superscript[y, l],
626 Description -> "Lepton Yukawa couplings"
627 },
628 yu == {
629 ParameterType -> Internal,
630 Indices -> {Index[Generation], Index[Generation]},
631 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
632 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
633 InteractionOrder -> {QED, 1},
634 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
635 TeX -> Superscript[y, u],
636 Description -> "Up-type Yukawa couplings"
637 },
638 yd == {
639 ParameterType -> Internal,
640 Indices -> {Index[Generation], Index[Generation]},
641 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
642 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
643 InteractionOrder -> {QED, 1},
644 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
645 TeX -> Superscript[y, d],
646 Description -> "Down-type Yukawa couplings"
647 },
648(* N. B. : only Cabibbo mixing! *)
649 CKM == {
650 ParameterType -> Internal,
651 Indices -> {Index[Generation], Index[Generation]},
652 Unitary -> True,
653 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
654 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
655 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
656 TeX -> Superscript[V,CKM],
657 Description -> "CKM-Matrix"}
658
659};
660
661(* ************************** *)
662(* ***** Lagrangian ***** *)
663(* ************************** *)
664
665LGauge := Block[{mu,nu,ii,aa},
666 -1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa] ];
667
668LFermions := Block[{mu},
669 I*(
670 QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + lRbar.Ga[mu].DC[lR, mu])];
671
672LHiggs := Block[{ii,mu},
673DC[Phibar[ii],mu] DC[Phi[ii],mu] + (MH^2/2) Phibar[ii] Phi[ii] - (MH^2/(2*vev^2)) Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]
674];
675
676LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk},
677
678 yuk = -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
679 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
680 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj];
681 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
682 yuk+HC[yuk]
683];
684
685LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
686 (* Pure gauge piece *)
687 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
688 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
689 LGhs = -ghGbar.del[DC[ghG,mu],mu];
690
691 (* Scalar pieces: see Peskin pages 739-742 *)
692 (* phi1 and phi2 are the real degrees of freedom of GP *)
693 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
694 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
695 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
696 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
697 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
698 doublet0 = {0, vev/Sqrt[2]};
699 Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
700 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
701 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
702
703LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0]];
704
705LSM:= LGauge + LFermions + LHiggs + LYukawa (*+ LGhost*);